The News of the World illegally targeted the missing schoolgirl Milly Dowler and her family in March 2002, interfering with police inquiries into her disappearance, an investigation by the Guardian has established.

Scotland Yard is investigating the episode, which is likely to put new pressure on the then editor of the paper, Rebekah Brooks, now Rupert Murdoch's chief executive in the UK; and the then deputy editor, Andy Coulson, who resigned in January as the prime minister's media adviser.

The Dowlers' family lawyer, Mark Lewis, this afternoon issued a statement describing the News of the World's activities as "heinous" and "despicable". He said this afternoon the Dowler family was now pursuing a damages claim against the News of the World.

Milly Dowler disappeared at the age of 13 on her way home in Walton-on-Thames, Surrey, on 21 March 2002.

Detectives from Scotland Yard's new inquiry into the phone hacking, Operation Weeting, are believed to have found evidence of the targeting of the Dowlers in a collection of 11,000 pages of notes kept by Glenn Mulcaire, the private investigator jailed for phone hacking on behalf of the News of the World.

In the last four weeks the Met officers have approached Surrey police and taken formal statements from some of those involved in the original inquiry, who were concerned about how News of the World journalists intercepted – and deleted – the voicemail messages of Milly Dowler.

The messages were deleted by journalists in the first few days after Milly's disappearance in order to free up space for more messages. As a result friends and relatives of Milly concluded wrongly that she might still be alive. Police feared evidence may have been destroyed.

The Guardian investigation has shown that, within a very short time of Milly vanishing, News of the World journalists reacted by engaging in what was standard practice in their newsroom: they hired private investigators to get them a story.

Their first step was simple, albeit illegal. Paperwork seen by the Guardian reveals that they paid a Hampshire private investigator, Steve Whittamore, to obtain home addresses and, where necessary, ex-directory phone numbers for any families called Dowler in the Walton area. The three addresses Whittamore found could be obtained lawfully on the electoral register. The two ex-directory numbers, however, were "blagged" illegally from British Telecom's confidential records by one of Whittamore's associates, John Gunning, who works from a base in Wiltshire. One of the ex-directory numbers was attributed by Whittamore to Milly's family home.

Then, with the help of its own full-time private investigator, Glenn Mulcaire, the News of the World started illegally intercepting mobile phone messages. Scotland Yard is now investigating evidence that the paper hacked directly into the voicemail of the missing girl's own phone. As her friends and parents called and left messages imploring Milly to get in touch with them, the News of the World was listening and recording their every private word.

But the journalists at the News of the World then encountered a problem. Milly's voicemail box filled up and would accept no more messages. Apparently thirsty for more information from more voicemails, the paper intervened – and deleted the messages that had been left in the first few days after her disappearance. According to one source, this had a devastating effect: when her friends and family called again and discovered that her voicemail had been cleared, they concluded that this must have been done by Milly herself and, therefore, that she must still be alive. But she was not. The interference created false hope and extra agony for those who were misled by it.

The Dowler family then granted an exclusive interview to the News of the World in which they talked about their hope, quite unaware that it had been falsely kindled by the newspaper's own intervention. Sally Dowler told the paper: "If Milly walked through the door, I don't think we'd be able to speak. We'd just weep tears of joy and give her a great big hug."

The deletion of the messages also caused difficulties for the police by confusing the picture when they had few leads to pursue. It also potentially destroyed valuable evidence.

According to one senior source familiar with the Surrey police investigation: "It can happen with abduction murders that the perpetrator will leave messages, asking the missing person to get in touch, as part of their efforts at concealment. We need those messages as evidence. Anybody who destroys that evidence is seriously interfering with the course of a police investigation."

The paper made little effort to conceal the hacking from its readers. On 14 April 2002 it published a story about a woman allegedly pretending to be Milly Dowler who had applied for a job with a recruitment agency: "It is thought the hoaxer even gave the agency Milly's real mobile number … the agency used the number to contact Milly when a job vacancy arose and left a message on her voicemail … it was on March 27, six days after Milly went missing, that the employment agency appears to have phoned her mobile."

The newspaper also made no effort to conceal its activity from Surrey police. After it had hacked the message from the recruitment agency on Milly's phone, the paper informed police about it.

It was Surrey detectives who established that the call was not intended for Milly Dowler. At the time, Surrey police suspected that phones belonging to detectives and to Milly's parents also were being targeted.

One of those who was involved in the original inquiry said: "We'd arrange landline calls. We didn't trust our mobiles."

However, they took no action against the News of the World, partly because their main focus was to find the missing schoolgirl and partly because this was only one example of tabloid misbehaviour. As one source close to the inquiry put it: "There was a hell of a lot of dirty stuff going on." Two earlier Yard inquiries had failed to investigate the relevant notes in Mulcaire's logs.

In a statement, the family's lawyer said the Dowlers were distressed at the revelation. "It is distress heaped upon tragedy to learn that the News of the World had no humanity at such a terrible time. The fact that they were prepared to act in such a heinous way that could have jeopardised the police investigation and give them false hope is despicable," Lewis said.

The News of the World's investigation was part of a long campaign against paedophiles championed by the then editor, Rebekah Brooks. The Labour MP Tom Watson last week told the House of Commons that four months after Milly Dowler's disappearance the News of the World had targeted one of the parents of the two 10-year-old Soham girls, Jessica Chapman and Holly Wells, who were abducted and murdered on 4 August 2002.

The behaviour of tabloid newspapers became an issue in the trial of Levi Bellfield, who last month was jailed for life for murdering Milly. A second charge, that he had attempted to abduct another Surrey schoolgirl, Rachel Cowles, had to be left on file after premature publicity by tabloids was held to have made it impossible for the jury to reach a fair verdict. The tabloids, however, focused their anger on Bellfield's defence lawyer, complaining that the questioning had caused unnecessary pain to Milly Dowler's parents.

Surrey police referred all questions on the subject to Scotland Yard, who said they could not discuss it.

The News of the World's parent company News International, part of Murdoch's media empire, said: "We have been co-operating fully with Operation Weeting since our voluntary disclosure in January restarted the investigation into illegal voicemail interception. This particular case is clearly a development of great concern and we will be conducting our own inquiry as a result. We will obviously co-operate fully with any police request on this should we be asked."

• The following was published on 12 December 2011 in the corrections and clarifications column: An article about the investigation into the abduction and death of Milly Dowler (News of the World hacked Milly Dowler's phone during police hunt, 5 July, page 1) stated that voicemail "messages were deleted by [NoW] journalists in the first few days after Milly's disappearance in order to free up space for more messages. As a result friends and relatives of Milly concluded wrongly that she might still be alive." Since this story was published new evidence – as reported in the Guardian of 10 December – has led the Metropolitan police to believe that this was unlikely to have been correct and that while the News of the World hacked Milly Dowler's phone the newspaper is unlikely to have been responsible for the deletion of a set of voicemails from the phone that caused her parents to have false hopes that she was alive, according to a Metropolitan police statement made to the Leveson inquiry on 12 December.